三维变形状态下Ⅰ型裂纹裂尖应力场结构的有限元分析*

本文用ADINA(Automatic Dynamical Incremental Nonlinear Analysis)有限元程序计算了三维变形条件下,幂硬化材料紧凑拉伸(CT)试样的应力应变场,并根据计算结果分析了Ⅰ型裂纹裂尖应力场的结构,发现在厚度方向的任一平面上,裂尖应力场的表达式都可写成r,θ坐标变量分离的形式,从而r的函数部分可展成罗朗级数,且三个正应力分量具有相同的数量级.这两个结论为从理论上求解Ⅰ型裂纹裂尖应力场的数学表达式提供了两个有根据的假设条件,可大大减化求解过程.

Analysis to the Stress Construction at the Vicinity of Crack Tip for Mode I Fracture in 3-D State Using Finite Element Method

The stresses and strains are calculated for CT specimen of power hardening material in 3-D deformation state using ADINAfinite element program, and the stress distribution at the vicinity of crack tip for Mode I fracture is analysed according to the results of calculation. It is found that the expression of stress can be written as the form of separation of variables of r and θ, then the function of r can be expanded in Laurant series. It is still found that the three normal stresses have the same order of magnitude. The conclusions offer two suppositions to obtain the theoretical expression of stress at the vicinity of crack tip for Mode I fracture with good ground, and the procedure of solution will be greatly simplified.